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In other words, the probability of a radioactive atom decaying within its half-life is 50%. [2] For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the ...
For example, the isotope copper-64, commonly used in medical research, has a half-life of 12.7 hours. If you inject a large group of animals at "time zero", but measure the radioactivity in their organs at two later times, the later groups must be "decay corrected" to adjust for the decay that has occurred between the two time points.
The half-life, t 1/2, is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value. The decay constant , λ " lambda ", the reciprocal of the mean lifetime (in s −1 ), sometimes referred to as simply decay rate .
The rules of radioactive decay may be used to convert activity to an actual number of atoms. They state that 1 Ci of radioactive atoms would follow the expression N (atoms) × λ (s −1) = 1 Ci = 3.7 × 10 10 Bq, and so N = 3.7 × 10 10 Bq / λ, where λ is the decay constant in s −1. Here are some examples, ordered by half-life:
The radioactive system behind hafnium–tungsten dating is a two-stage decay as follows: 182 72 Hf → 182 73 Ta e − ν e 182 73 Ta → 182 74 W e − ν e. The first decay has a half-life of 8.9 million years, while the second has a half-life of only 114 days, [7] such that the intermediate nuclide tantalum-182 (182 Ta) can effectively be ignored.
As an extreme example, the half-life of the isotope bismuth-209 is 2.01 × 10 19 years. The isotopes in beta-decay stable isobars that are also stable with regards to double beta decay with mass number A = 5, A = 8, 143 ≤ A ≤ 155, 160 ≤ A ≤ 162, and A ≥ 165 are theorized to undergo alpha decay.
Another example is the decay of hydrogen-3 into helium-3 with a half-life of about 12.3 years: 3 1 H → 3 2 He + e − + ν e. An example of positron emission (β + decay) is the decay of magnesium-23 into sodium-23 with a half-life of about 11.3 s: 23 12 Mg → 23 11 Na + e + + ν e
The decay scheme of a radioactive substance is a graphical presentation of all the transitions occurring in a decay, and of their relationships. Examples are shown below. It is useful to think of the decay scheme as placed in a coordinate system, where the vertical axis is energy, increasing from bottom to top, and the horizontal axis is the proton number, increasing from left to right.